Properties

Label 1440.3.j.b.1279.3
Level $1440$
Weight $3$
Character 1440.1279
Analytic conductor $39.237$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1440,3,Mod(1279,1440)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1440, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1440.1279");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1440.j (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(39.2371580679\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.1827904.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} + 9x^{4} + 14x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{9} \)
Twist minimal: no (minimal twist has level 160)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1279.3
Root \(1.37720i\) of defining polynomial
Character \(\chi\) \(=\) 1440.1279
Dual form 1440.3.j.b.1279.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.54778 - 4.75441i) q^{5} -0.206625 q^{7} +O(q^{10})\) \(q+(1.54778 - 4.75441i) q^{5} -0.206625 q^{7} -15.0176i q^{11} -11.6999i q^{13} +18.1911i q^{17} -19.3999i q^{19} +27.2242 q^{23} +(-20.2087 - 14.7176i) q^{25} -44.4175 q^{29} +20.3822i q^{31} +(-0.319810 + 0.982377i) q^{35} -18.1089i q^{37} +32.3043 q^{41} -4.06244 q^{43} -5.37588 q^{47} -48.9573 q^{49} +79.1703i q^{53} +(-71.3999 - 23.2440i) q^{55} -83.3999i q^{59} -36.7486 q^{61} +(-55.6262 - 18.1089i) q^{65} -4.51518 q^{67} -41.6530i q^{71} +41.5910i q^{73} +3.10301i q^{77} -15.5473i q^{79} +50.9862 q^{83} +(86.4880 + 28.1559i) q^{85} -10.8885 q^{89} +2.41749i q^{91} +(-92.2349 - 30.0268i) q^{95} -12.1559i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{5} + 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 2 q^{5} + 12 q^{7} + 68 q^{23} - 10 q^{25} - 44 q^{29} + 108 q^{35} + 68 q^{41} - 76 q^{43} - 268 q^{47} - 62 q^{49} - 288 q^{55} - 100 q^{61} + 308 q^{67} + 204 q^{83} - 32 q^{85} - 76 q^{89} + 32 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(641\) \(901\) \(991\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 1.54778 4.75441i 0.309556 0.950881i
\(6\) 0 0
\(7\) −0.206625 −0.0295178 −0.0147589 0.999891i \(-0.504698\pi\)
−0.0147589 + 0.999891i \(0.504698\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 15.0176i 1.36524i −0.730774 0.682619i \(-0.760841\pi\)
0.730774 0.682619i \(-0.239159\pi\)
\(12\) 0 0
\(13\) 11.6999i 0.899995i −0.893030 0.449998i \(-0.851425\pi\)
0.893030 0.449998i \(-0.148575\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 18.1911i 1.07007i 0.844831 + 0.535033i \(0.179701\pi\)
−0.844831 + 0.535033i \(0.820299\pi\)
\(18\) 0 0
\(19\) 19.3999i 1.02105i −0.859864 0.510523i \(-0.829452\pi\)
0.859864 0.510523i \(-0.170548\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 27.2242 1.18366 0.591831 0.806062i \(-0.298405\pi\)
0.591831 + 0.806062i \(0.298405\pi\)
\(24\) 0 0
\(25\) −20.2087 14.7176i −0.808350 0.588702i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −44.4175 −1.53164 −0.765819 0.643056i \(-0.777666\pi\)
−0.765819 + 0.643056i \(0.777666\pi\)
\(30\) 0 0
\(31\) 20.3822i 0.657492i 0.944418 + 0.328746i \(0.106626\pi\)
−0.944418 + 0.328746i \(0.893374\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.319810 + 0.982377i −0.00913742 + 0.0280679i
\(36\) 0 0
\(37\) 18.1089i 0.489431i −0.969595 0.244715i \(-0.921305\pi\)
0.969595 0.244715i \(-0.0786945\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 32.3043 0.787910 0.393955 0.919130i \(-0.371107\pi\)
0.393955 + 0.919130i \(0.371107\pi\)
\(42\) 0 0
\(43\) −4.06244 −0.0944753 −0.0472377 0.998884i \(-0.515042\pi\)
−0.0472377 + 0.998884i \(0.515042\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.37588 −0.114380 −0.0571902 0.998363i \(-0.518214\pi\)
−0.0571902 + 0.998363i \(0.518214\pi\)
\(48\) 0 0
\(49\) −48.9573 −0.999129
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 79.1703i 1.49378i 0.664948 + 0.746890i \(0.268454\pi\)
−0.664948 + 0.746890i \(0.731546\pi\)
\(54\) 0 0
\(55\) −71.3999 23.2440i −1.29818 0.422618i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 83.3999i 1.41356i −0.707435 0.706779i \(-0.750148\pi\)
0.707435 0.706779i \(-0.249852\pi\)
\(60\) 0 0
\(61\) −36.7486 −0.602435 −0.301218 0.953555i \(-0.597393\pi\)
−0.301218 + 0.953555i \(0.597393\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −55.6262 18.1089i −0.855788 0.278599i
\(66\) 0 0
\(67\) −4.51518 −0.0673907 −0.0336954 0.999432i \(-0.510728\pi\)
−0.0336954 + 0.999432i \(0.510728\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 41.6530i 0.586662i −0.956011 0.293331i \(-0.905236\pi\)
0.956011 0.293331i \(-0.0947638\pi\)
\(72\) 0 0
\(73\) 41.5910i 0.569740i 0.958566 + 0.284870i \(0.0919504\pi\)
−0.958566 + 0.284870i \(0.908050\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.10301i 0.0402988i
\(78\) 0 0
\(79\) 15.5473i 0.196801i −0.995147 0.0984004i \(-0.968627\pi\)
0.995147 0.0984004i \(-0.0313726\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 50.9862 0.614291 0.307146 0.951663i \(-0.400626\pi\)
0.307146 + 0.951663i \(0.400626\pi\)
\(84\) 0 0
\(85\) 86.4880 + 28.1559i 1.01751 + 0.331246i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −10.8885 −0.122343 −0.0611713 0.998127i \(-0.519484\pi\)
−0.0611713 + 0.998127i \(0.519484\pi\)
\(90\) 0 0
\(91\) 2.41749i 0.0265659i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −92.2349 30.0268i −0.970893 0.316071i
\(96\) 0 0
\(97\) 12.1559i 0.125318i −0.998035 0.0626592i \(-0.980042\pi\)
0.998035 0.0626592i \(-0.0199581\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −127.723 −1.26459 −0.632294 0.774728i \(-0.717887\pi\)
−0.632294 + 0.774728i \(0.717887\pi\)
\(102\) 0 0
\(103\) 4.77575 0.0463665 0.0231833 0.999731i \(-0.492620\pi\)
0.0231833 + 0.999731i \(0.492620\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −107.213 −1.00199 −0.500997 0.865449i \(-0.667033\pi\)
−0.500997 + 0.865449i \(0.667033\pi\)
\(108\) 0 0
\(109\) 53.6689 0.492376 0.246188 0.969222i \(-0.420822\pi\)
0.246188 + 0.969222i \(0.420822\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 20.5063i 0.181471i −0.995875 0.0907356i \(-0.971078\pi\)
0.995875 0.0907356i \(-0.0289218\pi\)
\(114\) 0 0
\(115\) 42.1372 129.435i 0.366410 1.12552i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3.75873i 0.0315860i
\(120\) 0 0
\(121\) −104.529 −0.863876
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −101.252 + 73.3010i −0.810016 + 0.586408i
\(126\) 0 0
\(127\) −138.477 −1.09037 −0.545184 0.838316i \(-0.683540\pi\)
−0.545184 + 0.838316i \(0.683540\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 219.105i 1.67256i −0.548304 0.836279i \(-0.684726\pi\)
0.548304 0.836279i \(-0.315274\pi\)
\(132\) 0 0
\(133\) 4.00849i 0.0301390i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 59.7821i 0.436366i 0.975908 + 0.218183i \(0.0700129\pi\)
−0.975908 + 0.218183i \(0.929987\pi\)
\(138\) 0 0
\(139\) 26.6524i 0.191744i −0.995394 0.0958718i \(-0.969436\pi\)
0.995394 0.0958718i \(-0.0305639\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −175.705 −1.22871
\(144\) 0 0
\(145\) −68.7486 + 211.179i −0.474128 + 1.45641i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −143.463 −0.962838 −0.481419 0.876490i \(-0.659879\pi\)
−0.481419 + 0.876490i \(0.659879\pi\)
\(150\) 0 0
\(151\) 83.4937i 0.552939i 0.961023 + 0.276469i \(0.0891644\pi\)
−0.961023 + 0.276469i \(0.910836\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 96.9055 + 31.5473i 0.625197 + 0.203531i
\(156\) 0 0
\(157\) 169.673i 1.08072i 0.841434 + 0.540360i \(0.181712\pi\)
−0.841434 + 0.540360i \(0.818288\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −5.62520 −0.0349391
\(162\) 0 0
\(163\) 275.478 1.69005 0.845026 0.534726i \(-0.179585\pi\)
0.845026 + 0.534726i \(0.179585\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −132.481 −0.793299 −0.396650 0.917970i \(-0.629827\pi\)
−0.396650 + 0.917970i \(0.629827\pi\)
\(168\) 0 0
\(169\) 32.1115 0.190009
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 272.614i 1.57580i −0.615801 0.787901i \(-0.711168\pi\)
0.615801 0.787901i \(-0.288832\pi\)
\(174\) 0 0
\(175\) 4.17562 + 3.04101i 0.0238607 + 0.0173772i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 157.523i 0.880014i 0.897994 + 0.440007i \(0.145024\pi\)
−0.897994 + 0.440007i \(0.854976\pi\)
\(180\) 0 0
\(181\) −335.063 −1.85118 −0.925590 0.378529i \(-0.876430\pi\)
−0.925590 + 0.378529i \(0.876430\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −86.0972 28.0287i −0.465391 0.151506i
\(186\) 0 0
\(187\) 273.187 1.46090
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 298.575i 1.56322i −0.623766 0.781611i \(-0.714398\pi\)
0.623766 0.781611i \(-0.285602\pi\)
\(192\) 0 0
\(193\) 191.915i 0.994376i −0.867643 0.497188i \(-0.834366\pi\)
0.867643 0.497188i \(-0.165634\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 59.2472i 0.300747i −0.988629 0.150374i \(-0.951952\pi\)
0.988629 0.150374i \(-0.0480477\pi\)
\(198\) 0 0
\(199\) 309.100i 1.55327i −0.629953 0.776633i \(-0.716926\pi\)
0.629953 0.776633i \(-0.283074\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 9.17775 0.0452106
\(204\) 0 0
\(205\) 50.0000 153.588i 0.243902 0.749209i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −291.340 −1.39397
\(210\) 0 0
\(211\) 205.693i 0.974850i −0.873165 0.487425i \(-0.837936\pi\)
0.873165 0.487425i \(-0.162064\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −6.28777 + 19.3145i −0.0292454 + 0.0898348i
\(216\) 0 0
\(217\) 4.21147i 0.0194077i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 212.835 0.963054
\(222\) 0 0
\(223\) −228.723 −1.02567 −0.512833 0.858488i \(-0.671404\pi\)
−0.512833 + 0.858488i \(0.671404\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 282.403 1.24407 0.622033 0.782991i \(-0.286307\pi\)
0.622033 + 0.782991i \(0.286307\pi\)
\(228\) 0 0
\(229\) 49.2525 0.215076 0.107538 0.994201i \(-0.465703\pi\)
0.107538 + 0.994201i \(0.465703\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 124.273i 0.533363i −0.963785 0.266681i \(-0.914073\pi\)
0.963785 0.266681i \(-0.0859271\pi\)
\(234\) 0 0
\(235\) −8.32069 + 25.5591i −0.0354072 + 0.108762i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 80.4527i 0.336622i −0.985734 0.168311i \(-0.946169\pi\)
0.985734 0.168311i \(-0.0538313\pi\)
\(240\) 0 0
\(241\) −1.20979 −0.00501988 −0.00250994 0.999997i \(-0.500799\pi\)
−0.00250994 + 0.999997i \(0.500799\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −75.7752 + 232.763i −0.309287 + 0.950053i
\(246\) 0 0
\(247\) −226.977 −0.918936
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 211.853i 0.844034i −0.906588 0.422017i \(-0.861322\pi\)
0.906588 0.422017i \(-0.138678\pi\)
\(252\) 0 0
\(253\) 408.843i 1.61598i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 182.646i 0.710685i 0.934736 + 0.355342i \(0.115636\pi\)
−0.934736 + 0.355342i \(0.884364\pi\)
\(258\) 0 0
\(259\) 3.74175i 0.0144469i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −74.6636 −0.283892 −0.141946 0.989874i \(-0.545336\pi\)
−0.141946 + 0.989874i \(0.545336\pi\)
\(264\) 0 0
\(265\) 376.408 + 122.538i 1.42041 + 0.462409i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 184.089 0.684344 0.342172 0.939637i \(-0.388837\pi\)
0.342172 + 0.939637i \(0.388837\pi\)
\(270\) 0 0
\(271\) 234.746i 0.866222i 0.901341 + 0.433111i \(0.142584\pi\)
−0.901341 + 0.433111i \(0.857416\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −221.023 + 303.487i −0.803719 + 1.10359i
\(276\) 0 0
\(277\) 452.208i 1.63252i 0.577684 + 0.816260i \(0.303957\pi\)
−0.577684 + 0.816260i \(0.696043\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 196.110 0.697900 0.348950 0.937141i \(-0.386538\pi\)
0.348950 + 0.937141i \(0.386538\pi\)
\(282\) 0 0
\(283\) 418.449 1.47862 0.739309 0.673366i \(-0.235152\pi\)
0.739309 + 0.673366i \(0.235152\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −6.67486 −0.0232574
\(288\) 0 0
\(289\) −41.9170 −0.145042
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 286.666i 0.978383i 0.872176 + 0.489191i \(0.162708\pi\)
−0.872176 + 0.489191i \(0.837292\pi\)
\(294\) 0 0
\(295\) −396.517 129.085i −1.34412 0.437575i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 318.522i 1.06529i
\(300\) 0 0
\(301\) 0.839400 0.00278870
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −56.8787 + 174.718i −0.186488 + 0.572844i
\(306\) 0 0
\(307\) −261.715 −0.852493 −0.426247 0.904607i \(-0.640164\pi\)
−0.426247 + 0.904607i \(0.640164\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 578.904i 1.86143i 0.365747 + 0.930714i \(0.380813\pi\)
−0.365747 + 0.930714i \(0.619187\pi\)
\(312\) 0 0
\(313\) 99.3124i 0.317292i −0.987336 0.158646i \(-0.949287\pi\)
0.987336 0.158646i \(-0.0507129\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 191.623i 0.604489i −0.953230 0.302245i \(-0.902264\pi\)
0.953230 0.302245i \(-0.0977359\pi\)
\(318\) 0 0
\(319\) 667.045i 2.09105i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 352.905 1.09259
\(324\) 0 0
\(325\) −172.194 + 236.441i −0.529829 + 0.727511i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.11079 0.00337626
\(330\) 0 0
\(331\) 530.187i 1.60177i 0.598816 + 0.800886i \(0.295638\pi\)
−0.598816 + 0.800886i \(0.704362\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −6.98851 + 21.4670i −0.0208612 + 0.0640806i
\(336\) 0 0
\(337\) 487.427i 1.44637i −0.690653 0.723186i \(-0.742677\pi\)
0.690653 0.723186i \(-0.257323\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 306.093 0.897633
\(342\) 0 0
\(343\) 20.2404 0.0590099
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 310.497 0.894804 0.447402 0.894333i \(-0.352349\pi\)
0.447402 + 0.894333i \(0.352349\pi\)
\(348\) 0 0
\(349\) −253.004 −0.724941 −0.362471 0.931995i \(-0.618067\pi\)
−0.362471 + 0.931995i \(0.618067\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 322.639i 0.913992i −0.889469 0.456996i \(-0.848925\pi\)
0.889469 0.456996i \(-0.151075\pi\)
\(354\) 0 0
\(355\) −198.035 64.4697i −0.557846 0.181605i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 254.975i 0.710236i 0.934822 + 0.355118i \(0.115559\pi\)
−0.934822 + 0.355118i \(0.884441\pi\)
\(360\) 0 0
\(361\) −15.3550 −0.0425347
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 197.740 + 64.3738i 0.541755 + 0.176366i
\(366\) 0 0
\(367\) −207.935 −0.566581 −0.283291 0.959034i \(-0.591426\pi\)
−0.283291 + 0.959034i \(0.591426\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 16.3585i 0.0440931i
\(372\) 0 0
\(373\) 203.826i 0.546450i −0.961950 0.273225i \(-0.911910\pi\)
0.961950 0.273225i \(-0.0880903\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 519.682i 1.37847i
\(378\) 0 0
\(379\) 454.099i 1.19815i −0.800692 0.599076i \(-0.795535\pi\)
0.800692 0.599076i \(-0.204465\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 541.569 1.41402 0.707009 0.707205i \(-0.250044\pi\)
0.707009 + 0.707205i \(0.250044\pi\)
\(384\) 0 0
\(385\) 14.7530 + 4.80278i 0.0383194 + 0.0124748i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 423.431 1.08851 0.544256 0.838919i \(-0.316812\pi\)
0.544256 + 0.838919i \(0.316812\pi\)
\(390\) 0 0
\(391\) 495.240i 1.26660i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −73.9180 24.0638i −0.187134 0.0609209i
\(396\) 0 0
\(397\) 11.7772i 0.0296654i −0.999890 0.0148327i \(-0.995278\pi\)
0.999890 0.0148327i \(-0.00472157\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −127.442 −0.317809 −0.158905 0.987294i \(-0.550796\pi\)
−0.158905 + 0.987294i \(0.550796\pi\)
\(402\) 0 0
\(403\) 238.471 0.591739
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −271.953 −0.668190
\(408\) 0 0
\(409\) 608.012 1.48658 0.743290 0.668969i \(-0.233264\pi\)
0.743290 + 0.668969i \(0.233264\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 17.2325i 0.0417251i
\(414\) 0 0
\(415\) 78.9155 242.409i 0.190158 0.584118i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 565.630i 1.34995i 0.737840 + 0.674976i \(0.235846\pi\)
−0.737840 + 0.674976i \(0.764154\pi\)
\(420\) 0 0
\(421\) 711.356 1.68968 0.844841 0.535018i \(-0.179695\pi\)
0.844841 + 0.535018i \(0.179695\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 267.729 367.620i 0.629950 0.864988i
\(426\) 0 0
\(427\) 7.59316 0.0177826
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 309.254i 0.717526i 0.933429 + 0.358763i \(0.116801\pi\)
−0.933429 + 0.358763i \(0.883199\pi\)
\(432\) 0 0
\(433\) 187.374i 0.432735i −0.976312 0.216368i \(-0.930579\pi\)
0.976312 0.216368i \(-0.0694210\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 528.147i 1.20857i
\(438\) 0 0
\(439\) 289.657i 0.659811i −0.944014 0.329906i \(-0.892983\pi\)
0.944014 0.329906i \(-0.107017\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 295.516 0.667079 0.333539 0.942736i \(-0.391757\pi\)
0.333539 + 0.942736i \(0.391757\pi\)
\(444\) 0 0
\(445\) −16.8530 + 51.7683i −0.0378719 + 0.116333i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 604.409 1.34612 0.673061 0.739587i \(-0.264979\pi\)
0.673061 + 0.739587i \(0.264979\pi\)
\(450\) 0 0
\(451\) 485.134i 1.07569i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 11.4937 + 3.74175i 0.0252610 + 0.00822363i
\(456\) 0 0
\(457\) 392.507i 0.858877i 0.903096 + 0.429438i \(0.141288\pi\)
−0.903096 + 0.429438i \(0.858712\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 400.277 0.868279 0.434139 0.900846i \(-0.357053\pi\)
0.434139 + 0.900846i \(0.357053\pi\)
\(462\) 0 0
\(463\) 732.679 1.58246 0.791230 0.611518i \(-0.209441\pi\)
0.791230 + 0.611518i \(0.209441\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −592.126 −1.26794 −0.633968 0.773360i \(-0.718575\pi\)
−0.633968 + 0.773360i \(0.718575\pi\)
\(468\) 0 0
\(469\) 0.932947 0.00198923
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 61.0082i 0.128981i
\(474\) 0 0
\(475\) −285.519 + 392.047i −0.601092 + 0.825362i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 309.151i 0.645409i 0.946500 + 0.322705i \(0.104592\pi\)
−0.946500 + 0.322705i \(0.895408\pi\)
\(480\) 0 0
\(481\) −211.873 −0.440485
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −57.7940 18.8146i −0.119163 0.0387931i
\(486\) 0 0
\(487\) −570.769 −1.17201 −0.586005 0.810307i \(-0.699300\pi\)
−0.586005 + 0.810307i \(0.699300\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 301.659i 0.614378i −0.951649 0.307189i \(-0.900612\pi\)
0.951649 0.307189i \(-0.0993883\pi\)
\(492\) 0 0
\(493\) 808.004i 1.63895i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 8.60653i 0.0173170i
\(498\) 0 0
\(499\) 517.758i 1.03759i 0.854898 + 0.518795i \(0.173619\pi\)
−0.854898 + 0.518795i \(0.826381\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 406.671 0.808491 0.404246 0.914650i \(-0.367534\pi\)
0.404246 + 0.914650i \(0.367534\pi\)
\(504\) 0 0
\(505\) −197.688 + 607.249i −0.391461 + 1.20247i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −627.097 −1.23202 −0.616009 0.787739i \(-0.711252\pi\)
−0.616009 + 0.787739i \(0.711252\pi\)
\(510\) 0 0
\(511\) 8.59372i 0.0168175i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 7.39182 22.7059i 0.0143530 0.0440891i
\(516\) 0 0
\(517\) 80.7330i 0.156157i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 111.743 0.214478 0.107239 0.994233i \(-0.465799\pi\)
0.107239 + 0.994233i \(0.465799\pi\)
\(522\) 0 0
\(523\) 769.813 1.47192 0.735959 0.677027i \(-0.236732\pi\)
0.735959 + 0.677027i \(0.236732\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −370.776 −0.703560
\(528\) 0 0
\(529\) 212.160 0.401058
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 377.958i 0.709115i
\(534\) 0 0
\(535\) −165.943 + 509.736i −0.310174 + 0.952778i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 735.222i 1.36405i
\(540\) 0 0
\(541\) −225.558 −0.416927 −0.208463 0.978030i \(-0.566846\pi\)
−0.208463 + 0.978030i \(0.566846\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 83.0678 255.164i 0.152418 0.468191i
\(546\) 0 0
\(547\) 882.346 1.61306 0.806532 0.591190i \(-0.201342\pi\)
0.806532 + 0.591190i \(0.201342\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 861.694i 1.56387i
\(552\) 0 0
\(553\) 3.21245i 0.00580913i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 303.119i 0.544199i −0.962269 0.272100i \(-0.912282\pi\)
0.962269 0.272100i \(-0.0877180\pi\)
\(558\) 0 0
\(559\) 47.5303i 0.0850273i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 344.003 0.611017 0.305508 0.952189i \(-0.401174\pi\)
0.305508 + 0.952189i \(0.401174\pi\)
\(564\) 0 0
\(565\) −97.4950 31.7392i −0.172558 0.0561756i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 228.925 0.402329 0.201165 0.979557i \(-0.435527\pi\)
0.201165 + 0.979557i \(0.435527\pi\)
\(570\) 0 0
\(571\) 371.169i 0.650033i −0.945708 0.325017i \(-0.894630\pi\)
0.945708 0.325017i \(-0.105370\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −550.168 400.674i −0.956814 0.696825i
\(576\) 0 0
\(577\) 580.289i 1.00570i −0.864374 0.502850i \(-0.832285\pi\)
0.864374 0.502850i \(-0.167715\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −10.5350 −0.0181325
\(582\) 0 0
\(583\) 1188.95 2.03936
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −65.0801 −0.110869 −0.0554345 0.998462i \(-0.517654\pi\)
−0.0554345 + 0.998462i \(0.517654\pi\)
\(588\) 0 0
\(589\) 395.413 0.671329
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1002.90i 1.69124i −0.533787 0.845619i \(-0.679232\pi\)
0.533787 0.845619i \(-0.320768\pi\)
\(594\) 0 0
\(595\) −17.8705 5.81770i −0.0300345 0.00977764i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 888.567i 1.48342i −0.670722 0.741709i \(-0.734016\pi\)
0.670722 0.741709i \(-0.265984\pi\)
\(600\) 0 0
\(601\) 132.065 0.219742 0.109871 0.993946i \(-0.464956\pi\)
0.109871 + 0.993946i \(0.464956\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −161.788 + 496.973i −0.267418 + 0.821443i
\(606\) 0 0
\(607\) 700.090 1.15336 0.576680 0.816970i \(-0.304348\pi\)
0.576680 + 0.816970i \(0.304348\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 62.8975i 0.102942i
\(612\) 0 0
\(613\) 727.420i 1.18666i 0.804961 + 0.593328i \(0.202186\pi\)
−0.804961 + 0.593328i \(0.797814\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 99.7137i 0.161611i −0.996730 0.0808053i \(-0.974251\pi\)
0.996730 0.0808053i \(-0.0257492\pi\)
\(618\) 0 0
\(619\) 721.349i 1.16535i 0.812707 + 0.582673i \(0.197993\pi\)
−0.812707 + 0.582673i \(0.802007\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2.24983 0.00361129
\(624\) 0 0
\(625\) 191.787 + 594.847i 0.306859 + 0.951755i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 329.422 0.523723
\(630\) 0 0
\(631\) 796.856i 1.26285i −0.775438 0.631423i \(-0.782471\pi\)
0.775438 0.631423i \(-0.217529\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −214.332 + 658.375i −0.337530 + 1.03681i
\(636\) 0 0
\(637\) 572.797i 0.899211i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −205.013 −0.319833 −0.159917 0.987131i \(-0.551123\pi\)
−0.159917 + 0.987131i \(0.551123\pi\)
\(642\) 0 0
\(643\) −495.044 −0.769897 −0.384949 0.922938i \(-0.625781\pi\)
−0.384949 + 0.922938i \(0.625781\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1121.84 1.73391 0.866953 0.498389i \(-0.166075\pi\)
0.866953 + 0.498389i \(0.166075\pi\)
\(648\) 0 0
\(649\) −1252.47 −1.92984
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 622.987i 0.954038i −0.878893 0.477019i \(-0.841717\pi\)
0.878893 0.477019i \(-0.158283\pi\)
\(654\) 0 0
\(655\) −1041.71 339.127i −1.59040 0.517751i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 264.030i 0.400653i 0.979729 + 0.200326i \(0.0642002\pi\)
−0.979729 + 0.200326i \(0.935800\pi\)
\(660\) 0 0
\(661\) 1285.15 1.94425 0.972124 0.234469i \(-0.0753352\pi\)
0.972124 + 0.234469i \(0.0753352\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 19.0580 + 6.20427i 0.0286586 + 0.00932972i
\(666\) 0 0
\(667\) −1209.23 −1.81294
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 551.876i 0.822468i
\(672\) 0 0
\(673\) 1244.16i 1.84868i −0.381565 0.924342i \(-0.624615\pi\)
0.381565 0.924342i \(-0.375385\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 963.335i 1.42295i 0.702713 + 0.711473i \(0.251972\pi\)
−0.702713 + 0.711473i \(0.748028\pi\)
\(678\) 0 0
\(679\) 2.51170i 0.00369912i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −770.819 −1.12858 −0.564289 0.825577i \(-0.690850\pi\)
−0.564289 + 0.825577i \(0.690850\pi\)
\(684\) 0 0
\(685\) 284.228 + 92.5296i 0.414932 + 0.135080i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 926.287 1.34439
\(690\) 0 0
\(691\) 408.765i 0.591555i −0.955257 0.295778i \(-0.904421\pi\)
0.955257 0.295778i \(-0.0955788\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −126.716 41.2520i −0.182325 0.0593554i
\(696\) 0 0
\(697\) 587.652i 0.843116i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1335.62 −1.90530 −0.952650 0.304068i \(-0.901655\pi\)
−0.952650 + 0.304068i \(0.901655\pi\)
\(702\) 0 0
\(703\) −351.311 −0.499731
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 26.3908 0.0373279
\(708\) 0 0
\(709\) 362.956 0.511927 0.255964 0.966686i \(-0.417607\pi\)
0.255964 + 0.966686i \(0.417607\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 554.891i 0.778249i
\(714\) 0 0
\(715\) −271.953 + 835.374i −0.380354 + 1.16836i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 648.098i 0.901388i −0.892679 0.450694i \(-0.851177\pi\)
0.892679 0.450694i \(-0.148823\pi\)
\(720\) 0 0
\(721\) −0.986788 −0.00136864
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 897.622 + 653.717i 1.23810 + 0.901679i
\(726\) 0 0
\(727\) 431.123 0.593017 0.296508 0.955030i \(-0.404178\pi\)
0.296508 + 0.955030i \(0.404178\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 73.9003i 0.101095i
\(732\) 0 0
\(733\) 1464.87i 1.99846i −0.0392126 0.999231i \(-0.512485\pi\)
0.0392126 0.999231i \(-0.487515\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 67.8073i 0.0920044i
\(738\) 0 0
\(739\) 99.1951i 0.134229i −0.997745 0.0671144i \(-0.978621\pi\)
0.997745 0.0671144i \(-0.0213793\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −602.719 −0.811196 −0.405598 0.914052i \(-0.632937\pi\)
−0.405598 + 0.914052i \(0.632937\pi\)
\(744\) 0 0
\(745\) −222.049 + 682.081i −0.298053 + 0.915545i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 22.1529 0.0295767
\(750\) 0 0
\(751\) 541.472i 0.721001i 0.932759 + 0.360501i \(0.117394\pi\)
−0.932759 + 0.360501i \(0.882606\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 396.963 + 129.230i 0.525779 + 0.171166i
\(756\) 0 0
\(757\) 1092.79i 1.44358i 0.692113 + 0.721789i \(0.256680\pi\)
−0.692113 + 0.721789i \(0.743320\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 18.7706 0.0246657 0.0123328 0.999924i \(-0.496074\pi\)
0.0123328 + 0.999924i \(0.496074\pi\)
\(762\) 0 0
\(763\) −11.0893 −0.0145338
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −975.773 −1.27219
\(768\) 0 0
\(769\) 39.0830 0.0508231 0.0254116 0.999677i \(-0.491910\pi\)
0.0254116 + 0.999677i \(0.491910\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 31.2171i 0.0403843i 0.999796 + 0.0201922i \(0.00642780\pi\)
−0.999796 + 0.0201922i \(0.993572\pi\)
\(774\) 0 0
\(775\) 299.977 411.900i 0.387067 0.531484i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 626.699i 0.804492i
\(780\) 0 0
\(781\) −625.529 −0.800933
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 806.695 + 262.617i 1.02764 + 0.334544i
\(786\) 0 0
\(787\) −988.563 −1.25612 −0.628058 0.778167i \(-0.716150\pi\)
−0.628058 + 0.778167i \(0.716150\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 4.23710i 0.00535663i
\(792\) 0 0
\(793\) 429.956i 0.542189i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 118.920i 0.149210i 0.997213 + 0.0746048i \(0.0237695\pi\)
−0.997213 + 0.0746048i \(0.976230\pi\)
\(798\) 0 0
\(799\) 97.7933i 0.122395i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 624.598 0.777831
\(804\) 0 0
\(805\) −8.70658 + 26.7445i −0.0108156 + 0.0332230i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1214.04 −1.50067 −0.750337 0.661056i \(-0.770109\pi\)
−0.750337 + 0.661056i \(0.770109\pi\)
\(810\) 0 0
\(811\) 706.666i 0.871351i −0.900104 0.435676i \(-0.856509\pi\)
0.900104 0.435676i \(-0.143491\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 426.380 1309.74i 0.523166 1.60704i
\(816\) 0 0
\(817\) 78.8108i 0.0964636i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −991.775 −1.20801 −0.604004 0.796981i \(-0.706429\pi\)
−0.604004 + 0.796981i \(0.706429\pi\)
\(822\) 0 0
\(823\) 523.998 0.636693 0.318347 0.947974i \(-0.396872\pi\)
0.318347 + 0.947974i \(0.396872\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −318.794 −0.385483 −0.192741 0.981250i \(-0.561738\pi\)
−0.192741 + 0.981250i \(0.561738\pi\)
\(828\) 0 0
\(829\) −1034.11 −1.24742 −0.623711 0.781655i \(-0.714376\pi\)
−0.623711 + 0.781655i \(0.714376\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 890.588i 1.06913i
\(834\) 0 0
\(835\) −205.052 + 629.868i −0.245571 + 0.754333i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 445.284i 0.530732i −0.964148 0.265366i \(-0.914507\pi\)
0.964148 0.265366i \(-0.0854928\pi\)
\(840\) 0 0
\(841\) 1131.91 1.34591
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 49.7016 152.671i 0.0588184 0.180676i
\(846\) 0 0
\(847\) 21.5983 0.0254997
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 493.002i 0.579321i
\(852\) 0 0
\(853\) 1200.49i 1.40737i −0.710513 0.703684i \(-0.751537\pi\)
0.710513 0.703684i \(-0.248463\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1223.15i 1.42724i 0.700531 + 0.713622i \(0.252946\pi\)
−0.700531 + 0.713622i \(0.747054\pi\)
\(858\) 0 0
\(859\) 210.033i 0.244509i −0.992499 0.122254i \(-0.960988\pi\)
0.992499 0.122254i \(-0.0390124\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1560.47 1.80819 0.904095 0.427333i \(-0.140547\pi\)
0.904095 + 0.427333i \(0.140547\pi\)
\(864\) 0 0
\(865\) −1296.12 421.947i −1.49840 0.487800i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −233.483 −0.268680
\(870\) 0 0
\(871\) 52.8273i 0.0606513i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 20.9211 15.1458i 0.0239099 0.0173095i
\(876\) 0 0
\(877\) 1011.66i 1.15354i −0.816906 0.576771i \(-0.804313\pi\)
0.816906 0.576771i \(-0.195687\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −266.455 −0.302446 −0.151223 0.988500i \(-0.548321\pi\)
−0.151223 + 0.988500i \(0.548321\pi\)
\(882\) 0 0
\(883\) −469.871 −0.532130 −0.266065 0.963955i \(-0.585724\pi\)
−0.266065 + 0.963955i \(0.585724\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 764.559 0.861961 0.430980 0.902361i \(-0.358168\pi\)
0.430980 + 0.902361i \(0.358168\pi\)
\(888\) 0 0
\(889\) 28.6127 0.0321853
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 104.291i 0.116788i
\(894\) 0 0
\(895\) 748.926 + 243.810i 0.836789 + 0.272414i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 905.328i 1.00704i
\(900\) 0 0
\(901\) −1440.20 −1.59844
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −518.605 + 1593.03i −0.573044 + 1.76025i
\(906\) 0 0
\(907\) −1333.20 −1.46990 −0.734948 0.678123i \(-0.762794\pi\)
−0.734948 + 0.678123i \(0.762794\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1496.11i 1.64227i 0.570736 + 0.821134i \(0.306658\pi\)
−0.570736 + 0.821134i \(0.693342\pi\)
\(912\) 0 0
\(913\) 765.691i 0.838654i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 45.2725i 0.0493702i
\(918\) 0 0
\(919\) 564.228i 0.613959i −0.951716 0.306980i \(-0.900682\pi\)
0.951716 0.306980i \(-0.0993183\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −487.337 −0.527993
\(924\) 0 0
\(925\) −266.519 + 365.959i −0.288129 + 0.395631i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1449.16 −1.55991 −0.779957 0.625833i \(-0.784759\pi\)
−0.779957 + 0.625833i \(0.784759\pi\)
\(930\) 0 0
\(931\) 949.765i 1.02016i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 422.834 1298.84i 0.452229 1.38914i
\(936\) 0 0
\(937\) 258.795i 0.276196i −0.990419 0.138098i \(-0.955901\pi\)
0.990419 0.138098i \(-0.0440989\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −20.3444 −0.0216200 −0.0108100 0.999942i \(-0.503441\pi\)
−0.0108100 + 0.999942i \(0.503441\pi\)
\(942\) 0 0
\(943\) 879.461 0.932620
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −613.539 −0.647876 −0.323938 0.946078i \(-0.605007\pi\)
−0.323938 + 0.946078i \(0.605007\pi\)
\(948\) 0 0
\(949\) 486.612 0.512763
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 81.6126i 0.0856376i 0.999083 + 0.0428188i \(0.0136338\pi\)
−0.999083 + 0.0428188i \(0.986366\pi\)
\(954\) 0 0
\(955\) −1419.55 462.129i −1.48644 0.483905i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 12.3525i 0.0128806i
\(960\) 0 0
\(961\) 545.564 0.567704
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −912.440 297.042i −0.945534 0.307815i
\(966\) 0 0
\(967\) −127.482 −0.131833 −0.0659165 0.997825i \(-0.520997\pi\)
−0.0659165 + 0.997825i \(0.520997\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1122.62i 1.15615i −0.815983 0.578076i \(-0.803804\pi\)
0.815983 0.578076i \(-0.196196\pi\)
\(972\) 0 0
\(973\) 5.50703i 0.00565985i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 424.837i 0.434838i −0.976078 0.217419i \(-0.930236\pi\)
0.976078 0.217419i \(-0.0697639\pi\)
\(978\) 0 0
\(979\) 163.519i 0.167027i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −663.324 −0.674795 −0.337398 0.941362i \(-0.609547\pi\)
−0.337398 + 0.941362i \(0.609547\pi\)
\(984\) 0 0
\(985\) −281.685 91.7017i −0.285975 0.0930982i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −110.597 −0.111827
\(990\) 0 0
\(991\) 1771.36i 1.78745i −0.448616 0.893724i \(-0.648083\pi\)
0.448616 0.893724i \(-0.351917\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −1469.59 478.419i −1.47697 0.480823i
\(996\) 0 0
\(997\) 447.066i 0.448411i 0.974542 + 0.224205i \(0.0719786\pi\)
−0.974542 + 0.224205i \(0.928021\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1440.3.j.b.1279.3 6
3.2 odd 2 160.3.h.b.159.6 yes 6
4.3 odd 2 1440.3.j.a.1279.3 6
5.4 even 2 1440.3.j.a.1279.4 6
12.11 even 2 160.3.h.a.159.2 yes 6
15.2 even 4 800.3.b.i.351.1 6
15.8 even 4 800.3.b.h.351.6 6
15.14 odd 2 160.3.h.a.159.1 6
20.19 odd 2 inner 1440.3.j.b.1279.4 6
24.5 odd 2 320.3.h.f.319.1 6
24.11 even 2 320.3.h.g.319.5 6
48.5 odd 4 1280.3.e.f.639.1 6
48.11 even 4 1280.3.e.g.639.6 6
48.29 odd 4 1280.3.e.h.639.6 6
48.35 even 4 1280.3.e.i.639.1 6
60.23 odd 4 800.3.b.h.351.1 6
60.47 odd 4 800.3.b.i.351.6 6
60.59 even 2 160.3.h.b.159.5 yes 6
120.29 odd 2 320.3.h.g.319.6 6
120.53 even 4 1600.3.b.v.1151.1 6
120.59 even 2 320.3.h.f.319.2 6
120.77 even 4 1600.3.b.w.1151.6 6
120.83 odd 4 1600.3.b.v.1151.6 6
120.107 odd 4 1600.3.b.w.1151.1 6
240.29 odd 4 1280.3.e.g.639.1 6
240.59 even 4 1280.3.e.h.639.1 6
240.149 odd 4 1280.3.e.i.639.6 6
240.179 even 4 1280.3.e.f.639.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.3.h.a.159.1 6 15.14 odd 2
160.3.h.a.159.2 yes 6 12.11 even 2
160.3.h.b.159.5 yes 6 60.59 even 2
160.3.h.b.159.6 yes 6 3.2 odd 2
320.3.h.f.319.1 6 24.5 odd 2
320.3.h.f.319.2 6 120.59 even 2
320.3.h.g.319.5 6 24.11 even 2
320.3.h.g.319.6 6 120.29 odd 2
800.3.b.h.351.1 6 60.23 odd 4
800.3.b.h.351.6 6 15.8 even 4
800.3.b.i.351.1 6 15.2 even 4
800.3.b.i.351.6 6 60.47 odd 4
1280.3.e.f.639.1 6 48.5 odd 4
1280.3.e.f.639.6 6 240.179 even 4
1280.3.e.g.639.1 6 240.29 odd 4
1280.3.e.g.639.6 6 48.11 even 4
1280.3.e.h.639.1 6 240.59 even 4
1280.3.e.h.639.6 6 48.29 odd 4
1280.3.e.i.639.1 6 48.35 even 4
1280.3.e.i.639.6 6 240.149 odd 4
1440.3.j.a.1279.3 6 4.3 odd 2
1440.3.j.a.1279.4 6 5.4 even 2
1440.3.j.b.1279.3 6 1.1 even 1 trivial
1440.3.j.b.1279.4 6 20.19 odd 2 inner
1600.3.b.v.1151.1 6 120.53 even 4
1600.3.b.v.1151.6 6 120.83 odd 4
1600.3.b.w.1151.1 6 120.107 odd 4
1600.3.b.w.1151.6 6 120.77 even 4